the boundarylayer due to the large adverse pressure gradient to turn the flow at the hinge. The heat transfer rates computed using two-dimensional DSMC simulations for di fferent times were compared with those obtained from the experiment and it was observed that the surface heating values at 0.1 ms are in good agreement with the experiment, especially in the region close to the tip the first wedge and at the second wedge surface, while in time the di fferences between the measured and calculated values become large . Furthermore, the size of the separation increased between 0.1 and 0.4 ms but later the separation point moves towards the downstream direction. It should be noted that the DSMC data presented in Figure 1(a) was obtained by averaging of the particle data in the 0.002 ms time interval. In previous work , the macro-parameter sampling was conducted in batches so that flow transients in the DSMC solution could be observed, but, the time evolution of the solution was found to depend on the size of the time window. In fact, the batch size should be small enough to capture the unsteadiness and large enough to reduce the statistical noise of the DSMC method. To investigate the time evolution of the temperature and the velocity values in the x- and y-directions more closely, numerical probes were placed at two critical locations, where the separation starts and ends, as shown in Figure 1(a) at locations 4 and 14. The probed data for location 4 that was obtained by sampling each timestep (1 ns) is shown in Figure 1(b). Note that the number of particles in the aforementioned locations was found to be around 70,000 which provides sufficient statistics for sampling in each timestep. As can be seen, the simulation does not reach steady state in a time interval of 1 ms. The structure of the separation region changes after 0.5 ms where the velocity values become positive again. Additionally, the pressure values (not shown) have a tendency to increase in time which may result in the relocation of the separation region.
Examination of the sensitivity of these turbulent RANS analysis methods to ﬂuid dynamic parametric variations relative to established correlations in conjunction to these vetted experiments help establish the degree and range of credibility for optimized design results of MDO pro- cedures with embedded turbulent RANS aerothermodynamic analysis. One such recent uncertainty analysis was accomplished by the present author (Brown, Refs. [2,3]) at the discrete conditions of a vetted database of hypersonic experiments (Marvin, Brown and Gnoﬀo, Ref. . How- ever, realized during the course of that study was that by considering only a limited number of ﬂuid conditions as described by a small se- lect group of experiments, no matter how well-behaved the experiments, leads to an incomplete picture of the analysis validity; rather, there is need to ensure that the proper physical trends are obeyed. Essentially, it is only when both the point-wise accuracy and the trend sensitivity of the turbulent RANS methods embedded in MDO methods are phys- ically correct that optimized design results from MDO procedures can be trusted as being valid. By point-wise accuracy, we mean accuracy of design relevant quantities such as separation extent, separation bubble pressure, peak pressure and peak heating at the discrete ﬂow parameters of the considered experiments, while by ‘trend sensitivity’ we mean the partial derivative or variation of these design relevant quantities with re- spect to small variations of the ﬂow parameters (typically Mach number, Reynolds number, shock strength, wall cooling, etc.) about the discrete conditions of these considered experiments.
The study of high-speed aerodynamics has received great attention in the past few decades due to the creation of many exciting projects in the supersonic and hypersonic flight regime. New weapons systems, reusable reentry vehicles, hypersonic airplanes, and scramjet engine design push forward the need for a better understanding of the nature of supersonic and hypersonic flows. In November 2004, NASA successfully tested the X-43A research aircraft, which flew to nearly Mach 9.8 at 110,000 feet powered by a scramjet. The X-43A, shown in Figure 1.1, is the first aircraft to prove the feasibility of high-speed air-breathing propulsion. The application of this technology to a practical aircraft could make long-distance and space travel more economical and safer. However, in order to make these leaps in technology, a great deal of data over a large range of supersonic and hypersonic flight conditions must be collected and understood. The success of such projects as the X-43A has and will continue to depend on the fundamental understanding of high-speed aerodynamics.
Aviation has come a long way since the Wright brother’s first flight, and in such a short amount of time. We now find that we are capable of not just leaving the ground but leaving the solar system entirely. However current methods of escaping the atmosphere are relatively crude. Often employing a brute force approach, using rockets and other low payload/high cost configurations. Alternatively, we could fly to escape velocity (approximately Mach 25) within the atmosphere and then glide to orbit on the kinetic energy we amassed. Current state of the art configurations, such as the Skylon project, use a compromise, flying to it’s flight ceiling and rocketing the remaining distance. Unfortunately we lack sufficient understanding of the extreme regimes encountered when travelling so high and so fast to build a Mach 25 vehicle.
The workshop was not the rst and certainly not the last time SBLI's have been examined both experimen- tally and numerically. Experiments by Holden and Babinsky  attempted SBLI ow control via a series of streamwise grooves and bumps, shown in Figs. 4 and 5, with hopes of smearing the shock footprint. They showed that the ow elds inherent with SBLI's are highly sensitive to geometry deviations, such as the slot and bump geometries, or for that matter any foreign debris or geometry imperfections. Another experiment by Holden and Babinsky  explored the use of vortex generators (VG's) for SBLI ow control. Two types were tested: wedge-shaped, more commonly known as micro-ramps, and counter rotating vanes. It was found that the use of the VG's greatly reduced the separation region of the SBLI interaction region, with the vane type VG's going as far as to eliminate the separation region completely. Experiments by Pitt Ford and Babinsky  as well as by Lapsa  also explored the eects of micro-ramps on SBLI ow elds. Pitt Ford and Babinsky showed that micro-ramps located upstream of the interaction region can break up the separation bubble but not completely eliminate it while increasing downstream velocities, shown in Fig. 6. Lapsa showed that the use of inverse micro-ramps can decrease the displacement thickness and thus allow for less separation around the interaction region.
on transonic wings, inlet instability and high thermal loads at supersonic and hypersonic vehicles. To examine the fun- damental relationships, the complexity of the applications is usually reduced by using canonical geometries such as 2-D compression ramps or reflected shocks on a flat plate. This approach resulted in a generally good understanding of stationary SWBLI (Babinsky and Harvey 2011). Also, the understanding of SWBLI unsteadiness due to flow separa- tion made progress in the recent years (Clemens and Naray- anaswamy 2014). However, relatively little attention was paid to investigate unsteady SWBLI with traveling shock fronts leading to flow separation and occurring, for exam- ple, in shock tubes or during ram-jet starts inside the inlet. In these cases, it is important to determine the time scales in which the flow adapts to new flow conditions. A better understanding of traveling shock fronts, which induce flow separation, can help to improve the modeling of phenomena like unstart of supersonic inlets. The authors, however, have no knowledge of fundamental research dedicated to analyze the influence of a traveling impinging shock front on a tur- bulent boundarylayer, which results in SWBLI movement with flow separation. To isolate this effect of a traveling shock front, all other flow parameter variations should be minimized by using a test rig with a canonical geometry, enabling a shock front with constant shock strength to travel uniformly over a well-defined supersonic boundarylayer.
An alternative to using conventional body-fitted grids in simulating boundary-layer control devices is the use of immersed-boundary (IB) methods, which is the focus of this work. An immersed-boundary method is a non-boundary-conforming method, in which the effects on the flow due to the boundary are somehow mimicked by use of proper conditions near the boundary. This can reduce to a great extent, the complexity involved in grid- generation or even grid-adaptation in simulating flows around complicated objects, especially when these objects are moving. Also the application of an immersed-boundary method allows for use of stretched Cartesian grids in many cases which in turn makes simulations of turbulent flows using high fidelity approaches like LES and DNS more feasible . Thus, the potential advantages of an IB method in the simulation of boundarylayer control devices include significant economy in the number of mesh points required to render the control device (compared with body-fitted meshes), ease with which different types of control devices can be interchanged and their effects assessed, and the ability to model moving control devices without mesh adaptation.
The number of faces per cell must be considered for two reasons. The first is that an element with more faces will require more computational time, and therefore will run slower than an element with less faces on a cell-per-cell basis. The second is that aligning cell faces with the direction of flow can help improve solution detail and convergence. It can be reasoned that the triangular cell would be preferred for the first criteria, while the polygonal cell would be preferred for the second. A good compromise is to use the trimmer mesher due to its lower face count and ability to orient the mesh in a given direction. However, with the goal of these simulations being that of boundarylayer development, orienting to one direction with the trimmer mesh results in a loss of resolution in the solution. Since computational resources are not a limiting factor for this analysis, the polygonal mesher is selected to improve the robustness of the solution.
It is becoming increasingly difficult to ignore the role of short duration high speed flow test facilities. Recent developments in the field of supersonic and hypersonic applications have led to a renewed interest in this kind of test facilities. Recently, researchers have shown an increased interest in high speed flow conditions which can be used to simulate the real conditions encountered by aerospace vehicles . So far, however, there has been little discussion about the characteristics of the flow process inside these test facilities. Furthermore, far too little attention has been paid to discuss the parameters which affect the velocity profile inside these test facility. Consequently, this has heightened the need for a comprehensive and an integral study which is aided by computer capabilities such as CFD technique. Part of the aim of this paper is to perform a CFD simulation that is able to reveal what is happening for the shock wave generated by high speed flow test facility. The main purpose of this study is to develop deeper understanding of all parameters which affect the shock wave velocity profile and pressure history inside the facility. The short duration hypersonic test facility has been developed recently at the College of Engineering, Universiti Tenaga Nasional (UNITEN). The facility is the first of its kind in Malaysia . It allows various researches to be done in the field of high speed supersonic and hypersonic flows. The maximum Mach number obtainable depends on the type of the driver and driven gases. It is shown that a mach number of 4 can be achieved if CO 2 is used as the driven gas and
For high speed air-breathing engines, knowledge of the point at which boundarylayer separation occurs limits the design pa- rameters. Shock wave/turbulent boundarylayerinteractions are a common occurrence in supersonic flows with almost any flow deflection accompanied by shock formation. Incident shock in- teractions occur when the shock that impinges on the boundarylayer is generated by an external source. These allow for the study of the interaction of bulk flow compression without the added effects of streamline curvature and hence they have been used for the experimental work in this paper. They are particu- larly important for scramjet studies which involve ducted flows where there is a requirement to add as much heat and pressure as possible. Unfortunately analytical means of modeling sep- arated flow are not advanced. CFD codes however have pro- gressed significantly to the point where several commercially available codes are capable of simulating hypersonic flows in reasonable time frames. When dealing with separated flows it is important to ensure the use of time accurate codes to capture upstream influences which is not possible with time marching codes. Turbulence models still need to be employed to approxi- mate turbulent effects and these are most probably the cause of a large proportion of inaccuracies. Choice of the most appropri- ate turbulence model is therefore very important. Two-equation models are far more accurate when predicting boundarylayer separation however for unseparated flows simple algebraic
smoothing filter (Savitzky & Golay 1964) was applied to reduce noise, adjusted so that frequencies below 100 kHz are unaffected, while those above 150 kHz are strongly damped. Examination of time traces showed structures propagating downstream in the boundarylayer at speeds of 77 % of the free-stream velocity. Such structures were repeatable in other tests and were observed starting from sensor TF07 (figure 2a). Probability density functions were obtained from the thin-film sensors. A selection is shown in figure 14, showing TF05, TF08B, TF10B and TF12B, which can be seen from figure 2 to be arranged along a streamwise line. The figure shows a clear progression from laminar to nearly fully turbulent flow. In contrast to the other cases, the HEG results at intermediate stations (for example, sensor TF10B) clearly show separate peaks around the laminar and turbulent mean values, indicating the presence of distinct turbulent spots in the flow. Such signals are similar to those observed by Schneider (1995) when the p.d.f. method was proposed and for this case the p.d.f. method is clearly preferred over direct detection methods with greater sensitivity to the choice of thresholds. Nevertheless the p.d.f. method still requires one parameter to be set and after consideration of all of the data, the level of q/ ˙ q ˙ lam = 3
These kinetic model equations were applied to the solution of one-dimensional, steady shock problems in a monatomic gas by Giddens et al.  and Segal et al . It was found that the ellipsoidal statistical model provided better agreement with experiment in comparison to the BGK model especially at low Mach number . Similarly, Andries et al.  studied the random particle method for simulation of weak shock compression problems and compared their solutions with Boltzmann, BGK, and ES-BGK models. They showed that the ES-BGK method, which uses corrected transport coefficients, gives results closer to the direct solution of the Boltzmann equation in comparison to BGK. However, it was observed that the rotational temperature was in better agreement when the BGK method was used. Kumar et al.  developed a statistical approach to the solution of the BGK and ES-BGK equations. Low-to-moderate Reynolds number conical nozzle flow expansions to vacuum were modeled with the ES-BGK approach and the results were compared with DSMC and NS solutions with velocity slip and temperature jump boundary conditions. The approach was found to be in good agreement with the benchmark DSMC results and were also found to be more efficient methods than DSMC in the continuum and near-continuum regimes. The ES-BGK was also found to be more accurate than NS solutions in the portions of the flow with rarefaction, such as the boundarylayer and the flow around the nozzle lip. Recently, finite-volume schemes for BGK and ES-BGK methods have been studied extensively. May et al.  proposed an approach to improve the efficiency and convergence of finite-volume schemes for three-dimensional geometries employing unstructured meshes. Moreover, Xu et al.  developed a finite-volume BGK formulation for the study of laminar hypersonic viscous flow where numerical fluxes are computed based on the velocity distribution function. The approach was applied to hypersonic flow over a double-cone geometry where SWBLIs, flow separation, and viscous/inviscid interaction are encountered. The heat fluxes obtained across body surfaces were found to be in good agreement with experiment.
decreases to 11.8 mm when the shock is downstream. This shows that the boundarylayer is thicker when the shock is upstream and thinner when it is downstream. This is a very intriguing result because it shows that the thickening / thinning mechanism proposed by McClure (1992) and Ünalmis and Dolling (1994) may indeed be correct. Recall that Beresh et al. (2002), in a PIV study, specifically addressed the thickening / thinning mechanism and found that it did not occur in Mach 5 compression ramp interactions. The difference between their study and the present one may be the difference in Mach numbers, but it is more likely to be due to the different particle seeding methods. Beresh et al. seeded their particles into the test section with an intrusive injector, and although they showed that the presence of the injector did not change the shock foot dynamics, it may have affected the correlation with the boundarylayer thickness. Their most important observation was that the shock motion is correlated with velocity fluctuations in the upstream boundarylayer. This mechanism will be tested with the current data below.
The model by Sun & Childs , which builds on the classical linear combination of the law of the wall and Coles’ wake function , has been used in the Cambridge facility for several years. Sun & Childs’s models is valid down to y + ≈ 100. For the buffer and viscous layers, the relationship proposed by Musker is used  to obtain complete solution for 0 ≤ y ≤ δ. The integral parameters can be calculated by simple numerical integration. A comprehensive investigation of the validity of this method has been performed by Titchener et al. . The main sources of errors were found to be the resolution of discrete data points and misalignment of the wall position. In particular, the number of points necessary for the error to be ≤ 5% is inversely proportional to the boundarylayer shape factor but approximately 20-30 points inside the boundarylayer are sufficient to achieve an error under 5% for a range of shape factors. This condition is generally satisfied in this investigation. Overall, the error is expected to be < 2% for the largest kinematic shape factor and < 5% for the thinnest, healthiest, boundary layers.
A mission relevant test problem is defined including free stream conditions for which the simulation uncertainty will be characterized. The governing equations and turbulence models are fully documented herein to remove any ambiguity of how models are formulated. A set of coarse grained uncertainty metrics are introduced to characterize the essential elements of a SWTBLI within a simulation. These metrics are also defined to easily capture their values from figures in the literature. Relevant experimental data on compression corners are reviewed and new simulations are executed with a variety of models and codes representative of the state of the art in 2006. The metrics are calculated for both existing and new simulations and a median value equal to 55% is computed for SWTBLI with separation on the basis of new, grid converged simulations. It is observed that grid converged solutions may enable sharper peaks in post shock pressure and heating as well as a larger extent of separation that may degrade comparisons with experimental data. Finally, new simulations are executed on the mission relevant problem to include gas chemistry perturbations in order to assess an overall uncertainty metric. Two appendices are also provided to present verification and validation data on a simpler flat plate problem.
Diffusers slow down the air entering the engines of supersonic aircraft to subsonic speeds to avoid damaging the engine. They typically do this by inducing shock waves prior to the engine inlet. In this report several diffuser geometries were modeled to cr eate oblique shock waves to reduce air speed with less stagnation pressure losses and drag than normal shock waves would create. These geometries include single ramp, double ramp, curved ramp, and a double ramp cone with external ramp and channel. This was done in Ansys Fluent using a refined mesh with an inflation layer along the diffuser surface. The CFD was run using a density based solver coupled with a turbulent model and the resulting stagnation pressure losses, drag, and boundarylayer separation were compared.
thane rubber product from Smooth-On Inc. with a Shore hardness of 50A. The steps to apply this material is similar to that of an epoxy. A 1:1 ratio of the two liquid components is thoroughly combined, and care is taken during the mixing process to ensure that no air bubbles are incorporated into the mixture which would lead to microbubbles that increased surface roughness. After mixing, the solution is poured flush into the recess while the model is on a level surface. The rubber is then left to harden over a few hours. To ensure that the rubber was fully cured, rubber-insert models were left for at least two days before any further modification were made for experiments. One advantage of this rubber is that there is negligible shrinkage upon drying. This particular rubber mixture is often used for production casting and naturally bonds to the flat plate once dry. For all the experiments in this study, the rubber surface was not externally pre-stressed. Fur- ther, schlieren imaging was performed to identify the presence of shock/Mach waves that may emanate from an uneven surface finish. No waves were detected within the rubber surface, confirming that the surface is indeed smooth and even.
The large-eddy simulation (LES) of a hypersonic flow passing a single-fin at Mach 5 and Re ∞ =3.7 × 107/m was conducted and the three-dimensional (3D) shock wave/turbulent boundarylayer interaction (SWTBLI) was studied in the present paper. This is probably a first reported LES of this kind of flows. The newly developed seventh order low-dissipation monotonicity-preserving scheme is used to solver the Euler fluxes and the dynamic Smagorinsky subgrid model is used to take account of the subgrid stress and heat flux. The shock system, flow separation structure, and turbulence characteristic are investigated by analyzing the LES data. The turbulence in the 3D SWTBLI is found to be dominated by small-scale wall turbulence, large-scale free shear turbulence, as well as the corner vortex in different regions. In the reverse flow, the streamwise elongated coherent structures are regenerated beneath the main separation vortex, almost immediately after the flow reattachment.
Lee (2001) presented a comprehensive review of shock-buffet studies, including physical models of the shock-buffet mechanism. These mechanisms were discussed for symmetrical circular-arc aerofoils at zero incidences and for supercritical aerofoils at high incidence angles with fully separated flows. During the examinations, Lee suggested that the buffet period is equal to the sum of the downstream and upstream wave’s motion time. Those pressure waves are produced either from the shock wave moving downstream to the trailing edge or the trailing edge boundarylayer and move upstream towards the shock. Estimating these motions by empirical evaluation over a single buffet cycle, Lee obtained good agreement with experiments.
The large-scale low-boom (LSLB) inlet test program investigated the large-scale wind-tunnel version of the supersonic axisymmetric-relaxed external compression inlet with vortex generators . Two inlet designs were examined in this study. The first was a dual-stream inlet with a nonzero cowl angle and splitter plate (Fig. 59a), whereas the second was a single-stream inlet featuring a zero-angle cowl (Fig. 59b). Both inlet designs included the same centerbody with a relaxed isentropic compression spike that redistributes a greater fraction of the compression process toward the terminal shock when compared to an axisymmetric isentropic surface. This design experiences a larger velocity gradient along the terminating shock from centerbody to cowl, but allows a lower cowl angle for reduced flow turning, thus reducing nacelle drag. This design was also shown numerically to increase supersonic aircraft performance and reduce sonic-boom overpressure as compared to traditional high-speed inlets . Computational and experimental analysis of a model in the NASA John H. Glenn Research Center (GRC) 1-by-1 ft supersonic wind tunnel showed that this mechanically simple inlet had two main restrictions: a tip-distortion increase due to a stronger normal shock at the cowl, and flow separation along the centerbody behind the base of the normal shock/boundary-layer interaction. To reduce separation and improve radial distortion at the aerodynamic interface plane (AIP), the use of vortex-generator, boundary- layer, flow-control devices was proposed [112-114].